Answer
a. $\forall x$, if x is an integer, then x is a rational number, but $\exists$ a rational number x such that x is not an integer.
b. $\forall x$ (Int(x) $\rightarrow$ Ratl(x)) $\land$ (Ratl(x) $\land$ ~Int(x))
Work Step by Step
Recall the definition of a universal statement: Let Q(x) be a predicate and D the domain of x. A universal statement is a statement of the form "$\forall x \in D, Q(x)$." It is defined to be true if, and only if, Q(x) is true for every x in D.
Recall the definition of an existential statement: Let Q(x) be a predicate and D the domain of x. An existential statement is a statement of the form "$\exists$ x \in D" such that $Q(x).$ It is defined to be true if, and only if, Q(x) is true for at least one x in D.
